The study of viral dynamics is one of the most important developments in recent HIV/AIDS research for understanding HIV pathogenesis and antiretroviral (ARV) therapies. However, most studies focused on short-term viral dynamics, and the models therein may not be applicable to long-term dynamics. Physiologically-based mathematical models and statistical methods play a critical role in AIDS research. Establishing the relationship of virologic responses (VR) to antiretroviral (ARV) therapy during long-term treatment is critical to the development of effective treatments. This is a challenging task because a practical model must incorporate multiple treatment factors including, but not limited to, drug concentration, drug adherence, drug susceptibility. Viral dynamics may be modeled through differential equations, but there has been only limited development in statistical methodologies for estimating and evaluating such differential equation models. The goals of this project are to develop viral dynamic models via systems of differential equations with time-varying coefficients but without a closed-form solution, and to apply them for characterizing long-term viral dynamics. Aim 1 of this proposal is to (a) study models for long-term HIV/T-cell dynamics and virologic/immunologic responses under ARV therapies, incorporating time-varying drug efficacy, pharmacokinetics, drug adherence and drug resistance;(b) develop flexible methods for fitting Bayesian nonlinear mixed-effects models which incorporate between-patient variations in dynamics;the basic principle of these methodologies were well established, but the applications of methods are nonetheless innovative within the context of a system of nonlinear differential equations of time-varying coefficient, but without a closed-form solution. Aim 2 is to apply the models and methods developed to AIDS clinical trials and to evaluate the models through simulations. It will focus on (a) validating the models and methods;(b) exploring pharmacodynamic relationships between VR and drug concentrations characterized by pharmacokinetic parameters in conjunction with other confounding factors such as drug adherence and resistance, and identifying clinical factors that are critical determinants of VR;(c) evaluating protocol designs used in AIDS clinical trials for their effectiveness in generating desired responses, therefore guiding the selection of ARV therapies with respect to level of dosing, number of subjects, timing and frequency of outcome monitoring. The proposed research will cast new lights on HIV dynamics in terms of the roles of clinical factors in mediating the long-term effectiveness of ARV therapies, hence a better understanding of HIV pathogenesis and long-term virologic responses, and will potentially lead to significant progress in understanding quantitative evaluation of clinical trial designs in response to existing therapies. Although this proposal will concentrate on HIV dynamics, the basic concept of longitudinal dynamic systems and the proposed methodologies in this project are generally applicable to dynamic systems in other fields such as PK/PD studies, biomedicine and public health as long as they meet the relevant technical specification-a set of differential equations. PUBLIC HEALTH RELEVANCE: The AIDS epidemic remains a grave public health threat world-wide. HIV dynamic studies have contributed significantly to the understanding of HIV pathogenesis and antiviral treatment strategies for AIDS patients. The overall goal of this project is to develop long-term HIV dynamic models and associated statistical methods for identifying clinical factors that are critical determinants of virological responses and for providing quantitative guidance to select and design antiretroviral treatments with respect to level of dosing, number of subjects, timing and frequency of outcome monitoring.